Question

Express the complex number in trigonometric form.

-3i

Answer 1

Think of `-3i` as `0-3i = 0 + (-3i)`

the last expression is in the form `a+bi` where `a = 0` and `b = -3`

Answer 2

You need to find r and theta

use

\[\Large r = \sqrt{a^2 + b^2}\]
\[\Large \theta = \arctan\left(\frac{b}{a}\right)\]

Answer 3

r = √0^2 + -3^2 = √0 + 9 = √9 = 3

Answer 4

yep `r = 3`

Answer 5

basically that says: "the point (0,-3) is 3 units away from the origin"

`0+(-3i)` can be plotted on the complex plane as the point (0,-3)

Answer 6

what would theta be?

Answer 7

im getting an error for theta..

Answer 8

yes you'll find that b/a = -3/0 = undefined

where is tangent undefined?

Answer 9

cos(x) = 0 ?

Answer 10

I guess a better way to find theta is by plotting where 0-3i is located

Answer 11

what angle is this?